Calculas help: Differentiability

[GiantsFanatic]

Graph each function on (-4,4), and identify the point(s) at which the function is not differentiable.

Graph F(X) = (X^2-2x+1)^1/3 on [4,-4] and Identify any points of discontinuity.

My attempt at a solution
I plugged in the F(x) equation on my calculator and I don't how to graph it on [-4,4]? I tried tracing the F(X) graph but I don't see the graph hitting the pt [-4.4] anywhere, am I doing this wrong?

[realmofotalk]

I don't know what you're doing wrong, but just to make sure the problem isn't a calculator reading error, I would put parentheses around x^2.

The other thing is that you said want to graph the F(x) equation on [4,-4] but then you're saying you don't know how to graph it on [-4,4]. That's two different points, unless you made a typo in your post.

[GiantsFanatic]

I tried that, same graph.

What the question is graph this equation on [-4,4], now is it implying that the F(x) that I graphed in my calc touches that point? If it does its continous? If it doesn't then it does not exist?

[bwitty24]

When you differentiate that equation you get:

(2(X-2))/(3(X^2-2X+1)^(2/3))

Therefore it is not differentiable at X=1 because you cannot divide by 0.

Does that help at all?

[GiantsFanatic]

Its not asking me to differentiate it, its just asking me to graph that equation on [-4,4], the part thats confusing me is the "on" part, does it mean if touches that point when you graph that equation?

[bwitty24]

The bracket means that points (4,4) (4,-4) (-4,-4) and (-4,4) are all included...if you want to go into flash chat now maybe i can clarify any questions.

[GiantsFanatic]

Okay I'll be in the flash chat

[realmofotalk]

I just thought of something. [-4,4] is an interval, not a point. There's no way that the point (-4,4) lies on that graph, because if you plug in -4 in that equation, you don't get the solution 4.

[GiantsFanatic]

I was reading the instructions, it says it has to be a piecewsie defined function.

[bwitty24]

The bracket means that points (4,4) (4,-4) (-4,-4) and (-4,4) are all included...if you want to go into flash chat now maybe i can clarify any questions.

[bwitty24]

ooo right my bad...those are just the x values not why values...therefore you should have a point (-4, blank) and (4,blank)

[realmofotalk]

Yes, you graph the equation on the interval [-4,4]. That's what the question meant by the "on" part.

[GiantsFanatic]

Oh wow, so I don't I plug in values of -4, -3..............3,4 into the X value of my function?

[realmofotalk]

There are finitely many (many many) rational numbers between -4 and 4, and not just the integers, so you definitely don't want to plug in explicit values. I think you're supposed to punch in what bwitty said: (-4, blank) and (blank, 4). He can probably give you the exact line to type.

[realmofotalk]

When you differentiate that equation you get:

(2(X-2))/(3(X^2-2X+1)^(2/3))

Therefore it is not differentiable at X=1 because you cannot divide by 0.

Bingo.

Ok, I just graphed the F(x). It's pretty clear to me that graph is a continuous parabola, so no points of discontinuity, but we can't tell where this graph is not differentiable (unlike an easy one with a corner or cusp). But bwitty answered that for ya.